Solve 0.48+sqrt{frac{1/1.0404}*(1.2-0.46)}{1+sqrt{1/1.0404}}=

$$\frac { 0.48 + \sqrt { \frac { 1 } { 1.0404 } } \times ( 1.2 - 0.46 ) } { 1 + \sqrt { \frac { 1 } { 1.0404 } } } =$$

Evaluate

$$\frac{1537}{2525}\approx 0.608712871$$

Solution Steps

Expand \frac{1}{1.0404} by multiplying both numerator and the denominator by 10000.

$$\frac{0.48+\sqrt{\frac{10000}{10404}}\left(1.2-0.46\right)}{1+\sqrt{\frac{1}{1.0404}}}$$

Reduce the fraction \frac{10000}{10404} to lowest terms by extracting and canceling out 4.

$$\frac{0.48+\sqrt{\frac{2500}{2601}}\left(1.2-0.46\right)}{1+\sqrt{\frac{1}{1.0404}}}$$

Rewrite the square root of the division \frac{2500}{2601} as the division of square roots \frac{\sqrt{2500}}{\sqrt{2601}}. Take the square root of both numerator and denominator.

$$\frac{0.48+\frac{50}{51}\left(1.2-0.46\right)}{1+\sqrt{\frac{1}{1.0404}}}$$

Subtract 0.46 from 1.2 to get 0.74.

$$\frac{0.48+\frac{50}{51}\times 0.74}{1+\sqrt{\frac{1}{1.0404}}}$$

Convert decimal number 0.74 to fraction \frac{74}{100}. Reduce the fraction \frac{74}{100} to lowest terms by extracting and canceling out 2.

$$\frac{0.48+\frac{50}{51}\times \frac{37}{50}}{1+\sqrt{\frac{1}{1.0404}}}$$

Multiply \frac{50}{51} times \frac{37}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{0.48+\frac{50\times 37}{51\times 50}}{1+\sqrt{\frac{1}{1.0404}}}$$

Cancel out 50 in both numerator and denominator.

$$\frac{0.48+\frac{37}{51}}{1+\sqrt{\frac{1}{1.0404}}}$$

Convert decimal number 0.48 to fraction \frac{48}{100}. Reduce the fraction \frac{48}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{12}{25}+\frac{37}{51}}{1+\sqrt{\frac{1}{1.0404}}}$$

Least common multiple of 25 and 51 is 1275. Convert \frac{12}{25} and \frac{37}{51} to fractions with denominator 1275.

$$\frac{\frac{612}{1275}+\frac{925}{1275}}{1+\sqrt{\frac{1}{1.0404}}}$$

Since \frac{612}{1275} and \frac{925}{1275} have the same denominator, add them by adding their numerators.

$$\frac{\frac{612+925}{1275}}{1+\sqrt{\frac{1}{1.0404}}}$$

Add 612 and 925 to get 1537.

$$\frac{\frac{1537}{1275}}{1+\sqrt{\frac{1}{1.0404}}}$$

Expand \frac{1}{1.0404} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{1537}{1275}}{1+\sqrt{\frac{10000}{10404}}}$$

Reduce the fraction \frac{10000}{10404} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1537}{1275}}{1+\sqrt{\frac{2500}{2601}}}$$

Rewrite the square root of the division \frac{2500}{2601} as the division of square roots \frac{\sqrt{2500}}{\sqrt{2601}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1537}{1275}}{1+\frac{50}{51}}$$

Convert 1 to fraction \frac{51}{51}.

$$\frac{\frac{1537}{1275}}{\frac{51}{51}+\frac{50}{51}}$$

Since \frac{51}{51} and \frac{50}{51} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1537}{1275}}{\frac{51+50}{51}}$$

Add 51 and 50 to get 101.

$$\frac{\frac{1537}{1275}}{\frac{101}{51}}$$

Divide \frac{1537}{1275} by \frac{101}{51} by multiplying \frac{1537}{1275} by the reciprocal of \frac{101}{51}.

$$\frac{1537}{1275}\times \frac{51}{101}$$

Multiply \frac{1537}{1275} times \frac{51}{101} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1537\times 51}{1275\times 101}$$

Do the multiplications in the fraction \frac{1537\times 51}{1275\times 101}.

$$\frac{78387}{128775}$$

Reduce the fraction \frac{78387}{128775} to lowest terms by extracting and canceling out 51.

$$\frac{1537}{2525}$$

Factor

$$\frac{29 \cdot 53}{101 \cdot 5 ^ {2}} = 0.6087128712871287$$